I don't know of any decent hire shops - only way I know to get a decent bike is to demo it. But others may have suggestions.

Closest trails to the city are Westgate Park (short loop under Westgate Bridge) or Yarra trails, starting at the Studley Park Rd bridge and heading upstream as far as you will. Both are easily accessible via bike from the city.

If you get some wheels one of us can give more precise instructions to the trails. I sometimes ride the Yarra trail home in the arvo getting to the bridge at about 4pm, sometimes later. So I could always show you the way upstream.